Inonu-Wigner Contractions of Kac-Moody Algebras

Details Inonu-Wigner Contractions of Kac-Moody Algebras Inonu-Wigner Contractions of Kac-Moody Algebras

1992-07-15

arxiv.org/abs/hep-th/9207057v1

J.Math.Phys. 34 (1993) 2059-2065

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, IMSc/92-26

Scientific paper

10.1063/1.530155

We discuss In\"on\"u-Wigner contractions of affine Kac-Moody algebras. We show that the Sugawara construction for the contracted affine algebra exists only for a fixed value of the level $k$, which is determined in terms of the dimension of the uncontracted part of the starting Lie algebra, and the quadratic Casimir in the adjoint representation. Further, we discuss contractions of $G/H$ coset spaces, and obtain an affine {\it translation} algebra, which yields a Virasoro algebra (via a GKO construction) with a central charge given by $dim(G/H)$.

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